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On the One-Way Function Candidate Proposed by Goldreich

2014
*
ACM Transactions on Computation Theory
*

*Goldreich*[2000]

*proposed*a

*candidate*

*one*-

*way*

*function*based

*on*a bipartite graph of small right-degree d, where

*the*vertices

*on*

*the*left (resp. right) represent input (resp. output) bits of

*the*

*function*... Inverting this

*function*as a

*one*-

*way*

*function*

*by*definition means finding an element in

*the*preimage of output of this

*function*for a random input. We bound

*the*expected size of this preimage. ... INTRODUCTION

*Goldreich*[2000]

*proposed*a

*candidate*

*one*-

*way*

*function*based

*on*expanders. ...

##
###
Page 10251 of Mathematical Reviews Vol. , Issue 2004m
[page]

2004
*
Mathematical Reviews
*

We

*propose*two natural*candidate*quantum Yao principles, a ‘weak’ and a ‘strong’*one*. ... If*the**one*-*way**function*acts*on*n-bit strings then*the*overhead in*the*reduction is*by*a factor of O(n/e*) in*the*classical case but only*by*a factor of O(1/e) in*the*quantum case, where 4+ is*the*probability ...##
###
The Complexity of Public-Key Cryptography
[chapter]

2017
*
Tutorials on the Foundations of Cryptography
*

We discuss

doi:10.1007/978-3-319-57048-8_2
fatcat:74ecqky6sraifpvfnylqxc6jom
*the*computational assumptions that have been used as bases for public-key encryption schemes, and*the*types of evidence we have for*the*veracity of these assumptions. ... We survey*the*computational foundations for public-key cryptography. ... Thus, if this algorithm cannot be improved to work in an optimal number of samples and polynomial time, then*one*-*way**functions*exist. 10 Goldreich's*One*-*Way**Function**Candidate**Goldreich*has*proposed*...##
###
Text Encryption using Lattice-Based Cryptography

2014
*
IOSR Journal of Computer Engineering
*

There are strong indications that these problems will remain secure under

doi:10.9790/0661-1628148151
fatcat:3rj53rojr5ek7h3syfc2kc6cxu
*the*assumption of*the*availability of quantum computers, unlike both*the*integer-factorization and discrete logarithm problems ... In this paper,*the*author will explore various methods to improve*the*practicality of lattice-based cryptosystems (GGH Encryption scheme) and to optimize*the*algorithm that make up these cryptosystems ...*The**Goldreich*-Goldwasser-Halevi (GGH) cryptosystem makes use of*the*fact that*the*closest vector problem can be a hard problem.It uses a trapdoor*one*-*way**function*that is relying*on**the*difficulty of lattice ...##
###
Concentration of the number of solutions of random planted CSPs and Goldreich's one-way candidates
[article]

2015
*
arXiv
*
pre-print

*The*result is also extended to a more general class of random planted CSPs; in particular, it is shown that

*the*number of pre-images for

*the*

*Goldreich*

*one*-

*way*

*function*model concentrates for some choices ... Specifically, if F^*_k(α,n) is a random k-SAT formula

*on*n variables, with clause density α and with a uniformly drawn planted solution, there exists a

*function*ϕ_k(·) such that, besides for some α in ... Impagliazzo for suggesting

*the*

*Goldreich*

*one*-

*way*

*function*model to

*the*first author, as well as A. Montanari for stimulating discussions. ...

##
###
A Candidate Counterexample to the Easy Cylinders Conjecture
[chapter]

2011
*
Lecture Notes in Computer Science
*

Our suggestion builds

doi:10.1007/978-3-642-22670-0_16
fatcat:yfthdakkcvgsbdpkvzbuulunbu
*on**the**candidate**one*-*way**function*based*on*expander graphs (see ECCC, TR00-090), and essentially consists of iterating this*function*polynomially many times. ... We present a*candidate*counterexample to*the*easy cylinders conjecture, which was recently suggested*by*Manindra Agrawal and Osamu Watanabe (see ECCC, TR09-019). ... Agrawal and Watanabe noted that all popular*candidates**one*-*way**functions*have easy cylinders. ...##
###
Candidate One-Way Functions and One-Way Permutations Based on Quasigroup String Transformations
[article]

2005
*
arXiv
*
pre-print

In this paper we

arXiv:cs/0510018v1
fatcat:gjczxwmsc5d53ompvopnjcss4q
*propose*a definition and construction of a new family of*one*-*way**candidate**functions*R_N:Q^N → Q^N, where Q={0,1,...,s-1} is an alphabet with s elements. ... table that defines them (a Latin Square) in order to check*the*satisfiability for*the*initial conditions, thus making them natural*candidates*for*one*-*way**functions*. ... There are also some*one*-*way**functions**candidates*based*on*sphere-packing problems and coding theory such as*the**proposals*from*Goldreich*, Krawczyk and Luby in [4] . ...##
###
One Way Functions –Conjecture, Status, Applications and Future Research Scope

2016
*
International Journal of Computer Applications
*

This paper presents

doi:10.5120/ijca2016912126
fatcat:jttkqoy3ercupctqpyqmtyphsu
*the*features and limitations of*proposed**candidate**functions*, and*the*implications of proof of*one**way**functions*conjecture. ...*The*conjecture that*one**way**function*exists is an open problem,*the*resolution of which holds*the*key for*the*solution of many unsolved problems in mathematics and cryptography. ... Over*the*years, various*candidate**functions*have been*proposed*as*one**way**functions*, which have withstand*the*rigorous cryptanalysis tests and extensive research for finding their inverse and have been ...##
###
Paillier's trapdoor function hides Θ(n) bits

2011
*
Science China Information Sciences
*

In this paper, we re-examine

doi:10.1007/s11432-011-4269-9
fatcat:6hjigkssefhydaak22trdtp2ai
*the*bit security of Paillier's trapdoor*function*. ... For*the*simultaneous security, we prove that n number of*the*class c's bits are simultaneously hard-core under*the*standard assumption, where n is*the*length of c. ... Acknowledgements This work is partially supported*by**the*National Natural Science Foundation of China (Grant No. 60970154), and*the*National Basic Research Program of China (Grant No. 2007CB311202). ...##
###
Query Complexity and Error Tolerance of Witness Finding Algorithms
[article]

2012
*
Electronic colloquium on computational complexity
*

We

dblp:journals/eccc/KawachiRW12
fatcat:qelcfhdzgzbatibowj3ktftt6y
*propose*an abstract framework for studying search-to-decision reductions for NP. ... Specifically, we study*the*following witness finding problem: for a hidden nonempty set W ⊆ {0, 1} n ,*the*goal is to output a witness in W with constant probability*by*making randomized queries of*the*... AK was supported*by**the*Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B) No.21300002. ...##
###
On a Family of Minimal Candidate One-way Functions and One-way Permutations

2009
*
International Journal of Network Security
*

In this paper we

dblp:journals/ijnsec/Gligoroski09
fatcat:aodljg6jkfhehll2rt7kg56qei
*propose*a definition and construction of a new family of*one*-*way**candidate**functions*R N : Q N → Q N , where Q = {0, 1, . . . , s − 1} is an alphabet with s elements. ... In order to achieve computational workload equivalent to*the*exhaustive key search of an n-bit key for inversion of RSA or Diffie-Hellman*one*-*way**candidate**functions**the*length of their arguments have ... There are also some*one*-*way**functions**candidates*based*on*sphere-packing problems and coding theory such as*the**proposals*from*Goldreich*, Krawczyk and Luby in [5] . ...##
###
Some facets of complexity theory and cryptography: A five-lecture tutorial

2002
*
ACM Computing Surveys
*

A

doi:10.1145/592642.592646
fatcat:qogelhnxlzerhmyeru6q3xcioa
*function*is*one*-*way*if it is easy to compute, but hard to invert. We discuss*the*notion of*one*-*way**functions*both in a cryptographic and in a complexity-theoretic setting. ... Particular attention is paid to cryptographic protocols and*the*problem of constructing key components of protocols such as*one*-*way**functions*. ... I thank Kari Pasanen for being a great tutor of this tutorial, for carefully proofreading a preliminary draft of this article, and in particular for subletting his summer house*on*an island of scenic Lake ...##
###
Chosen ciphertext attacks on lattice-based public key encryption and modern (non-quantum) cryptography in a quantum environment

2006
*
Theoretical Computer Science
*

Modern cryptography is based

doi:10.1016/j.tcs.2006.07.060
fatcat:7fd2bjvqorgmhmacoiyjoxjqoy
*on*various building blocks such as*one**way**functions*with or without trapdoors, pseudo-random*functions*,*one**way*permutations with or without trapdoors, etc. ... About half a decade agoAjtai and Dwork (and later*on*, also*Goldreich*, Goldwasser and Halevi)*proposed*a public key cryptosystem that has a proven security under a plausible complexity assumption. ... This work was supported in part*by**the*Israel MOD Research and Technology Unit. ...##
###
Simpler Session-Key Generation from Short Random Passwords
[chapter]

2004
*
Lecture Notes in Computer Science
*

*The*security bound achieved

*by*our protocol is somewhat worse than

*the*GL protocol. ... We present a simplification of

*the*

*Goldreich*-Lindell (GL) protocol and analysis for

*the*special case when

*the*dictionary is of

*the*form D = {0, 1} d , i.e.

*the*password is a short random string (like an ... We are also grateful to Mihir Bellare for pointing out

*the*extension of our protocol to arbitrary dictionaries in

*the*common random string model. ...

##
###
Goldreich's One-Way Function Candidate and Myopic Backtracking Algorithms
[chapter]

2009
*
Lecture Notes in Computer Science
*

*Goldreich*(ECCC 2000)

*proposed*a

*candidate*

*one*-

*way*

*function*construction which is parameterized

*by*

*the*choice of a small predicate (over d = O(1) variables) and of a bipartite expanding graph of right-degree ...

*The*

*function*is computed

*by*labeling

*the*n vertices

*on*

*the*left with

*the*bits of

*the*input, labeling each of

*the*n vertices

*on*

*the*right with

*the*value of

*the*predicate applied to

*the*neighbors, and outputting ...

*The*original version of this chapter was revised:

*The*copyright line was incorrect. This has been corrected.

*The*Erratum to this chapter is available at DOI: 10.1007/978-3-642-00457-5_36 ...

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